We prove an asymptotic Lipschitz estimate for value functions of tug-of-war games with varying probabilities defined in Ω ⊂ ℝn. The method of the proof is based on a game-theoretic idea to estimate the value of a related ...
This thesis studies local and global regularity properties of a stochastic
two-player zero-sum game called tug-of-war. In particular, we study value
functions of the game locally as well as globally, that is, close to ...
Heino, Joonas(International Statistical Institute; Bernoulli Society for Mathematical Statistics and Probability, 2018)
We show that a uniform measure density condition implies game regularity for all 2 < p < ∞ in a stochastic game called “tug-of-war with noise”. The proof utilizes suitable choices of strategies combined with estimates for ...
Attouchi, Amal; Luiro, Hannes; Parviainen, Mikko(Society for Industrial and Applied Mathematics, 2021)
We define a random step size tug-of-war game and show that the gradient of a value function exists almost everywhere. We also prove that the gradients of value functions are uniformly bounded and converge weakly to the ...
We obtain an asymptotic Hölder estimate for functions satisfying a dynamic programming principle arising from a so-called ellipsoid process. By the ellipsoid process we mean a generalization of the random walk where the ...
